1. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 STRUCTURE, DIPOLE MOMENTS, POLARIZABILITIES, AND MOLECULAR SPIN ORBIT OF STRONG DIPOLAR ALKALI DIATOMICS Mireille Aymar, Olivier Dulieu Laboratoire Aimé Cotton, CNRS and Université d’Orsay, France PhD’s: Johannes Deiglmayr (U. Freiburg/ LAC Orsay), Andreas Gerdes (U. Hannover/ LAC Orsay), Sihem Azizi (U. Tlemcen) until 2005 Coll. with F. Spiegelman (Lab. de Physique et Chimie Quantiques, Toulouse) Other members of the group: N. Bouloufa, A. Crubellier, R. Osseni, M. Raoult COMOL HPRN-CT-2002-00290 Interferences and Quantum Aplications French-German University

2. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 MOTIVATIONS for such computations:  Guide or interpret cold atom photoassociation and cold molecule formation experiments, as well as standard laser spectroscopy (gas phase, He-clusters..)  Discover new processes for cold molecule formation; calculation of rates  Alkali dimers: systems of choice experimentally  Numerous quantum chemistry results on potential curves for homo- and heteronuclear diatomics (Lyon, Beirut, Monastir, Temple U., Riga-Moscow, Kaiserslautern…)  Only few data on permanent or transition dipole moments, static polarisabilities, spin-orbit couplings  No systematic quantitative comparison on the accuracy/consistency between various methods

3. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 REVIEW of OUR RECENT WORK  New series of systematic calculations of electronic properties for ALL alkali pairs involving Li, Na, K, Rb, Cs: potential curves, permanent and transition dipole moments, static polarizabilities, spin-orbit couplings  New results for Francium compounds (Fr 2, RbFr, CsFr)  Method based on the CIPSI package (Configuration Interaction by Perturbation of a multiconfiguration wave function Selected Iteratively, Laboratoire de Physique Quantique, Toulouse, France). (B. Huron et al., J. Chem. Phys. 58, 5745)  Spin-orbit calculations relying on a diabatization procedure with no adjusted parameter  Automated calculations and data treatment for ALL Pairs, ALL symmetries, ALL interatomic distances, ALL transitions  Convergence and accuracy checked against size of basis sets, and through detailed comparison with other methods

4. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 CALCULATION STEPS (in short)  ATOM:  The ionic core described by an ℓ -dependent (large core) pseudopotentiel [1]  Effective one-electron atom described by a Gaussian basis set.  Pseudopotential parameters adjusted to reproduce energies and valence orbitals of an all-electron Hartree-Fock (HF) calculation.  Fr: new pseudopotential with parameters adjusted to reproduce spin-averaged orbitals and energies of an all-electron relativistic Dirac-Fock (DF) calculation [2].  Core polarization: ℓ-dependent effective core polarization potential (ECPP) [3], involving (expt’l [4]) ion polarizabilities, and cut-off radii (fitted on atomic spectrum) to prevent divergence at short distances  MOLECULE:  One-electron molecular orbitals (MO) determined via Restricted Hartree-Fock calculation, including ECPP’s: potential curves for molecular ions  Full (2 electron) configuration interaction (CI): potential curves, permanent and transition dipole moments.  Computation in an external electric field: static polarizabilities [1] P. Durand and J.C. Barthelat, Theor. chim. Acta, 38, 283 (1975) [2] J.P. Desclaux, Comp. Phys. Comm., 9, 31 (1975) [3] M. Foucrault, P. Millié, and J.P. Daudey, J. Chem. Phys. 96, 1257 (1992) [4] J.N. Wilson and R.M. Curtis, J. Chem. Phys. 74, 187 (1970)

5. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 RESULTS: POTENTIAL CURVES excellent overall agreement with previous work from Lyon group and coll. (same parameters, same basis) Core-core interaction Extended basis: improved description of atomic energies. Example for Cs : [7s4p5d1f]/[6s4p4d1f] extended to [9s6p6d4f]. Potential wells deeper by about 20cm -1 for molecular ions, 70-200cm -1 for neutrals. Corresponds to the limits of accuracy for such calculations (core-core interaction,…) 5s+6s 5s+6p 5p+6s

6. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 R (a.u.) Dipole moment (Debye) RESULTS: PERMANENT DIPOLE MOMENTS X1+X1+ LiCs KRb JCP, 122, 204302 (2005) + - light heavy R-dependence, v-dependence Less than 1% variation with basis size Most of these results were not available elsewhere This work Park et al (2000) X1+X1+ a3+a3+ Kotochigova et al 2004) This work Kotochigova et al, PRA 68, 022501 (2003) Park et al, Chem. Phys, 257, 135 (2000) KRb

7. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 Permanent dipole moments - + light heavy + - Cs Fr Rb Cs Rb Fr Ground state Metastable triplet state RESULTS: FRANCIUM COMPOUNDS Aymar, Dulieu, Spiegelman JPB, 39, S905 (2006)

8. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 RESULTS: TRANSITION DIPOLE MOMENTS Comparison with: Multi-partitioning perturbation theory, Zaitsevskii et al, PRA 63, 052504 (2001) NaRb Mol. Phys., in press (NaK, NaRb, NaCs) Accurate check of the consistency of electronic wave functions among various methods

9. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 RESULTS: STATIC POLARIZABILITIES (1) Homonuclear alkali pairs Heteronuclear alkali pairs RbCs KCs LiCs KRb

10. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 RESULTS: STATIC POLARIZABILITIES (2) Average polarizability Anisotropy LiCs

11. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 important contribution for heavy alkalis Mainly included with effective (*** system-dependent ***) operators Published potential curves available for LiCs, NaCs, KCs, KRb, RbCs, Cs 2. Almost no data on R-dependent SO couplings for dynamics purpose MOLECULAR SPIN-ORBIT Calculate potential curves without spin-orbit operator Define states at large internuclear distance as reference basis Calculate unitary transformation to represent molecular states in this reference basis  effective Hamiltonian in „atomic“ basis Add spin-orbit coupling in this basis (asymptotic fine structure) Rediagonalize Hamiltonian provides adiabatic curves OR rotate back to molecular basis provides coupling matrix elements Same procedure for all systems, for an arbitrary number of asymptotes OUR IDEA

12. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 First results for Cs 2 states correlated to the 6s+6p and 6s+5d asymptotes No spin-orbit interaction With spin-orbit interaction (rediagonalization)

13. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 R-dependent spin-orbit matrix elements ( after rotation back to molecular basis ) Comparison with Spies’ data (1990) for 0 g - ( 3  g + - 3  g ) symmetry

14. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 Cs 2 0 g -

15. International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 Perspectives of this work: Spin-orbit couplings for all alkali pairs (LiRb, LiCs, RbCs, Rb 2,…). Mixed alkali/alkaline-earth ions… and neutrals… Triatomic alkali ions… and neutrals… Dynamics… atom/molecule photoassociation… …and hopefully interaction with experimentalists… There « could be » possibilities for PhD/postdoc positions… Today’s published results from our group: NaK, NaRb, NaCs : M. Aymar and O. Dulieu, submitted to Molecular Physics (2007) Rb 2 : J. Lozeille et al (Orsay+ Pise + Storrs) Eur. Phys. J. D 39, 261 (2006); V. Horvatic et al (Orsay+ Zagreb), Phys. Rev. A, 75, 032512 (2007). KRb: Beuc et al (Zagreb+Orsay), J. Phys. B, 39, S1191 (2006) Fr 2, RbFr, CsFr: Aymar, Dulieu, Spiegelman J. Phys. B, 39, S905 (2006) All other systems in preparation ( including alkali hydrides )